FIRST OFF, I TAKE NO CREDIT FOR THIS. This was taken directly from another post here. (And then Aaro!edited.)

Phantom:

He appears in Nakano at these coordinates: X18 & Y23/24, but only around New Moon from 0:00 to 6:00. So, if you want to take him down, you have to be quick. He's one of the easier boss fights. His minions consist of Mutated Spectres and Mutated Shadows, both of which are aggressive. Lightning/Hama are the main elements to use here, as they are all weak against them.

You can also get the Phantom plug-in from an NPC in Ueno or Souhouzan (don't remember which), but it's from a quest. To activate it, you need a Surt or an Immature (Inexperienced) Surt. You must have either devil summoned if you want the quest from the NPC.

Raphael:

He appears in Shibuya at these coordinates: X20 & Y23, at "supposedly" random times (since there doesn't seem to be an exact time that he appears). The only weakness he has is Mudo, so he can be difficult if you don't have a gunner or a melee with a mudo-based weapon with you. Avoid using Wind, since he nullifies that element. When he enters, he looks like he has the Confused status-ailment. Even with that, he is still a major threat since his attacks can heavily damage you. His minions consist of Mutated Powers, Avatar of Form Angels (stronger than the normal form), and Avatar of Form Powers (that know Megidoron!). Raphael and all Powers can detect you from far, far away, so be prepared.

You can also get the Raphael plug-in from an NPC at the Arcadia Gates in Shinagawa, but it's part of a quest. To activate it, you need Uriel or Immature (Inexperienced) Uriel. You must have either devil summoned if you want the quest from the NPC.

Nyarlathotep:

There are actually "two" bosses, but the 2nd one has a 20% chance of appearing. (Aaro!note~ : I don't know what Pearz plans on doing to "correct" this 20% error. But read the comment.) Both of these fights are rather difficult if unprepared, as both bosses have anti-knockback.

Both of them appear at Nakano at these coordinates: X21 & Y24, during full moon (the entire phase.) However, you need a "Shining Trapozehedron" to summon him. The first phase is "Burning Three-Eyed" Nyarlathotep, and he has no weaknesses. Avoid using Maryoku-based (Aaro!note~ : "maryoku" is Japanese for "magic") attacks (it absorbs), and Hama/Mudo-based attacks ( it resists). However, any elemental weapon is fair game. His minions consist of Nightmare Black Oozes (weak to Lightning and Hama), ones that can use Fog Breath and the Area Counter (so watch out for those). Use Grand Curse (Aaro!note~ : Rho says this is probably Erosion Hex) for the Oozes since they can be rather troublesome.

If you're lucky, "Crawling Chaos" Nyarlathotep will appear (with the same resistances and weaknesses). The minions are smaller, weaker versions of the main boss minions. Make sure to avoid using magic-based weapons/skills/spells, as they can absorb them, and avoid Hama/Mudo-based weapons as well.

"Crawling Chaos" Nyarlathotep is the most important one, as he drops a special item that is needed to give you the Nyarlathotep plug-in. There is no need to activate a quest for the plug-in (probably due to the fact that it's a real pain to get the Shining Trapozehedron).

Valhalla - This system is simple. Kill a player for 2 points, and kill a pet for 1 point. The problem (or maybe it's a good thing) is that the match is small (max 5v5), so the winner is almost always pre-determined, by which team has the "best" player. This makes a lot of people quit the second they join, knowing it's hopeless and there's no point in losing GP. You must do these matches to get over 1100GP, as Fate matches cap at that. The BP gain is small, so it's not worth your time to do this for BP.

Fate - This system caps your GP at 1100, but gives amazing amounts of BP for the winning team.

Since it's just easier to explain with the map, here you go.The numbers represent how many points you gain per tick (each tick is exactly 30 seconds). When you initially capture a spot, you get whatever point number is there instantly. As you hold a spot longer, the points you gain will increase. The bars beside the number signify how much points extra you get per tick. So, for example, with the #5 spot on this map, you would gain 5-8-11-14, and so on (also making it the best spot to hold in this match). Basically, the longer you hold the spot, the more points it adds up. If you lose the spot even once, it resets back down to beginning, so it's important to defend these locations.

Other small notes: the surprise events in Fate are stupid events that cause more harm than it supposedly helps.You can buy the 1k HP cures for 5BP each, and so it's worth investing in.The 600kBP weapons are nearly impossible to obtain, as supposedly the top BP player on the JP server is only at 191kBP.

Last Note about PVP: If you see Xay, then run - he will 2-shot you (Delorean then Agi shot). D: ^_^